Question

A fixed volume of iron is drawn into a wire of length 'L'
The extension 'x' produced in the wire by a constant force
'F' is proportional to
(a) 1/L^2
(b)1/L
(c)L^2
(d)L​

Answer 1

Answer:

(b) 1/L,is the answer

Explanation:

because the volume is fixed and the force applied is constant

Answer 2

Given;

1. Fixed volume of iron is used to draw wire of length 'L'.
2. Extension 'x' is produced in the wire by constant force 'f'.

To find;

1. F is proportional to

Solution;

1. Young's modulus = {(Force/Area) / (Change in length ℓ   /Initial length L)}
2. ∴ Y = (FL / Aℓ)
3. Change in length=x
4. On rearranging 2, x=  (F × L)/ (A × Y)
5. Multiplying and dividing by L in rhs of 4.
6. x= (F×L²)/(A×L×Y)
7. But Area × Length= Volume.
8. Equation 6 becomes x= (F×L²)/(Y×V).
9. Y is a constant. F is given constant. Volume also remains constant.

Answer;

Thus we see that x α L².